Police arrive at a murder scene at 1:00 AM and immediately record the body\'s te
ID: 3029774 • Letter: P
Question
Police arrive at a murder scene at 1:00 AM and immediately record the body's temperature which was 90 degree F. At 3:00 AM, after thoroughly inspecting and fingerprinting the area, they again took the temperature of the body which had dropped to 86 degree F. The temperature of the crime scene has remained at a constant 75 degree F. Determine when the person was murdered. (Assume that the victim was healthy at the time of death. That is, assume that the temperature of the body at the time of death was 98.6 degree F.) The person was murdered at (Do not round until the final answer. Then round to the nearest minute as needed.)Explanation / Answer
applying newtons law of cooling
T(t) = Ts + ( To - Ts) e^-kt
Ts is temperature of the surrounding
To is initial temperature
plugging the values in the formula
T(t) = 75 + ( 90 - 75) e^-kt = 75 + 15e^-kt
temperature recorded at 3am was 86 ( in 2 hours temperature has dropped to 86)
86 = 75 + 15e^-k(2)
86-75 = 15e^-2k
.7333 = e^-2k
taking natural log on both sides
ln (.7333) = -2k
k = .1550
therefore, find t when body temperature was normal that is 98.6
98.6 = 70 + 15e^-.1550t
98.6-70 = 15e^(-.1550t)
1.9066 = e^(-.1550t )
ln 1.9066 = -.1550t
t = - 4.163
this indicates that teh death was approximately 4 hours before the temperature was taken
the death was around 9 pm